Shear modulus measures the rigidity of solid materials and is calculated by dividing shear stress by shear strain. It is expressed in gigapascals and indicates how much force is needed to deform a material. Elastic materials like rubber use the modulus of elasticity, which measures how much a material can stretch before permanent deformation. Young’s modulus is a measure of linear stress, while the modulus of mass measures the elasticity of a solid when pressure is applied from all sides.
Shear modulus, also often referred to as modulus of stiffness or modulus of torsion, is a measure of the rigid or rigid nature of different types of solid materials. It is derived from the material’s ratio of its shear stress value to its shear strain value. Shear stress is a value of how much force is applied to a square area of a material, usually measured in pressure values of pascals. Strain is the amount of material strain under stress divided by its original length. The shear modulus value is always a positive number and is expressed as an amount of force per unit area, which is usually recorded as metric gigapascals (GPa) because the values are more practical than the English equivalents.
Since gigapascals equal billions of pascals of force per unit area, shear modulus numbers can sometimes seem deceptively small. An example of how large shear modulus values can be is demonstrated when they are converted to British values of pounds per square inch (lb/in2). Diamond is estimated to have a modulus of stiffness of 478 GPa (69,328,039 lb/in2), pure aluminum is estimated to have a modulus of 26 GPa (3,770,981 lb/in2), and rubber ranges from 0.0002 to 0.001 GPa (29 to 145 lb/in2 ). To make these units more practical with English numerals, the practice is to express them in kips per square inch, where one kip equals 1,000 pounds of weight.
The harder a substance is, the higher its shear modulus value, depending on the ambient temperature when the value is measured. As the value of the shear modulus increases, this indicates that a much greater amount of force or stress is required to deform or deform it along the plane of the direction of force. The strain values themselves tend to be quite small, however, in calculations, because strain is just a measure of how much a solid material strains before it cracks or breaks. Most solids such as metals will only stretch a small amount before breaking.
The exception to this limitation on small strain values are elastic materials such as rubber, which can stretch much before degrading. These materials are often measured instead using the shear modulus of elasticity, which is also a ratio of stress to strain. Values for modulus of elasticity on materials are based on how much a material can be stretched before it experiences permanent deformation.
Modulus of elasticity is often the same measure as Young’s modulus, which specifically is a measure of linear stress on a solid defined as longitudinal strain versus longitudinal stress. Another closely related value in this series of measurements is the modulus of mass, which takes the Young’s modulus and applies it to all three dimensions in space. The mass modulus measures the elasticity of a solid when the pressure to deform it is universally applied from all sides and is the opposite of what happens when a material is compressed. It is a volumetric stress value divided by volumetric strain and can be visualized in an example as what would happen to a uniform solid under internal pressure when placed in a vacuum, which would cause it to expand in all directions.
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